Sains Malaysiana 42(7)(2013):
989–997
Lengkung Peralihan Licin dengan Kuartik Bezier Satahan
(Smooth Transition Curve by Planar Bezier Quartic)
Azhar
Ahmad
Fakulti
Sains Dan Matematik, Universiti Pendidikan Sultan Idris, 35900 Tanjung Malim,
Perak,
Malaysia
Jamaludin
Md Ali
Sekolah
Sains Matematik, Universiti Sains Malaysia, 11800 Minden, Pulau Pinang
Malaysia
Diserahkan:
21 Julai 2011/Diterima: 10 Februari 2013
ABSTRAK
ABSTRAK
Kertas ini membincangkan satu keluarga lengkung
peralihan satahan licin yang dibina menggunakan dua lingkaran kuartik Bezier. Lingkaran kuartik yang
diperkenalkan ini mempunyai enam darjah kebebasan yang memberi kelebihan untuk
mempelbagaikan rupa bentuk lingkaran di dalam selangnya. Kelicinan adalah dirujuk melalui ciri-ciri keselanjaran geometri G2 dan kelengkungan monoton
yang dimiliki oleh sesuatu lengkung peralihan. Oleh sebab lengkungan ini
tidak memiliki sebarang juring, gelung dan titik lengkok balas, di samping
tanpa perubahan kelengkungan yang mendadak maka ia amat sesuai untuk aplikasi
tertentu dalam Reka Bentuk Berbantukan Komputer (RBK) bagi memenuhi
keperluan estatis serta kepentingan fungsinya seperti reka bentuk produk
industri, trajektori robot tidak holonomi dan juga reka bentuk mendatar
landasan kereta api serta lebuh raya. Sebagai suatu
perwakilan polinomial, lingkaran kuartik Bezier ini mampu digabungjalinkan ke
dalam sistem RBK yang kebanyakannya berasaskan perwakilan NURBS (nonuniform rational B-splines).
Kata kunci: Kelengkungan monoton; lengkung peralihan; lingkaran
kuartik bezier
ABSTRACT
This paper reports on a family of smooth transition curve rendered
by a pair of Bezier quartic spiral. The family of Bezier quartic spiral form which was introduced has six degrees of freedom and
will give advantage on diversity of the transition curve in the given
constraints. Fair curves often referred on geometrical continuity G2 and
monotonically of curvature of the transition curves. Since these curves have no
cusps, loops and the inflection points, and free from abrupt chance of
curvature, therefore it is suitable for some particular application in Computer
Aided Design (CAD)
in terms of aesthetical and functional values, especially in the industrial
products design, trajectory of non-holonomic robot, as well as the horizontal
route designs of railways and highways. Since Bezier quartic spiral is
polynomial, it can be conveniently incorporated in CAD systems in the form
of NURBS (nonuniform
rational B-splines) representation.
Keywords: Bezier quartic spiral; monotone
curvature; transition curve
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*Pengarang
untuk surat-menyurat; email: azhar.ahmad@fsmt.upsi.edu.my
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